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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) 2: * 3: * -- LAPACK routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER UPLO 10: INTEGER INFO, KB, LDA, LDW, N, NB 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: COMPLEX*16 A( LDA, * ), W( LDW, * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * ZLAHEF computes a partial factorization of a complex Hermitian 21: * matrix A using the Bunch-Kaufman diagonal pivoting method. The 22: * partial factorization has the form: 23: * 24: * A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: 25: * ( 0 U22 ) ( 0 D ) ( U12' U22' ) 26: * 27: * A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' 28: * ( L21 I ) ( 0 A22 ) ( 0 I ) 29: * 30: * where the order of D is at most NB. The actual order is returned in 31: * the argument KB, and is either NB or NB-1, or N if N <= NB. 32: * Note that U' denotes the conjugate transpose of U. 33: * 34: * ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code 35: * (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or 36: * A22 (if UPLO = 'L'). 37: * 38: * Arguments 39: * ========= 40: * 41: * UPLO (input) CHARACTER*1 42: * Specifies whether the upper or lower triangular part of the 43: * Hermitian matrix A is stored: 44: * = 'U': Upper triangular 45: * = 'L': Lower triangular 46: * 47: * N (input) INTEGER 48: * The order of the matrix A. N >= 0. 49: * 50: * NB (input) INTEGER 51: * The maximum number of columns of the matrix A that should be 52: * factored. NB should be at least 2 to allow for 2-by-2 pivot 53: * blocks. 54: * 55: * KB (output) INTEGER 56: * The number of columns of A that were actually factored. 57: * KB is either NB-1 or NB, or N if N <= NB. 58: * 59: * A (input/output) COMPLEX*16 array, dimension (LDA,N) 60: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading 61: * n-by-n upper triangular part of A contains the upper 62: * triangular part of the matrix A, and the strictly lower 63: * triangular part of A is not referenced. If UPLO = 'L', the 64: * leading n-by-n lower triangular part of A contains the lower 65: * triangular part of the matrix A, and the strictly upper 66: * triangular part of A is not referenced. 67: * On exit, A contains details of the partial factorization. 68: * 69: * LDA (input) INTEGER 70: * The leading dimension of the array A. LDA >= max(1,N). 71: * 72: * IPIV (output) INTEGER array, dimension (N) 73: * Details of the interchanges and the block structure of D. 74: * If UPLO = 'U', only the last KB elements of IPIV are set; 75: * if UPLO = 'L', only the first KB elements are set. 76: * 77: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were 78: * interchanged and D(k,k) is a 1-by-1 diagonal block. 79: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and 80: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) 81: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = 82: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were 83: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 84: * 85: * W (workspace) COMPLEX*16 array, dimension (LDW,NB) 86: * 87: * LDW (input) INTEGER 88: * The leading dimension of the array W. LDW >= max(1,N). 89: * 90: * INFO (output) INTEGER 91: * = 0: successful exit 92: * > 0: if INFO = k, D(k,k) is exactly zero. The factorization 93: * has been completed, but the block diagonal matrix D is 94: * exactly singular. 95: * 96: * ===================================================================== 97: * 98: * .. Parameters .. 99: DOUBLE PRECISION ZERO, ONE 100: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 101: COMPLEX*16 CONE 102: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 103: DOUBLE PRECISION EIGHT, SEVTEN 104: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 ) 105: * .. 106: * .. Local Scalars .. 107: INTEGER IMAX, J, JB, JJ, JMAX, JP, K, KK, KKW, KP, 108: $ KSTEP, KW 109: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, R1, ROWMAX, T 110: COMPLEX*16 D11, D21, D22, Z 111: * .. 112: * .. External Functions .. 113: LOGICAL LSAME 114: INTEGER IZAMAX 115: EXTERNAL LSAME, IZAMAX 116: * .. 117: * .. External Subroutines .. 118: EXTERNAL ZCOPY, ZDSCAL, ZGEMM, ZGEMV, ZLACGV, ZSWAP 119: * .. 120: * .. Intrinsic Functions .. 121: INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SQRT 122: * .. 123: * .. Statement Functions .. 124: DOUBLE PRECISION CABS1 125: * .. 126: * .. Statement Function definitions .. 127: CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) ) 128: * .. 129: * .. Executable Statements .. 130: * 131: INFO = 0 132: * 133: * Initialize ALPHA for use in choosing pivot block size. 134: * 135: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT 136: * 137: IF( LSAME( UPLO, 'U' ) ) THEN 138: * 139: * Factorize the trailing columns of A using the upper triangle 140: * of A and working backwards, and compute the matrix W = U12*D 141: * for use in updating A11 (note that conjg(W) is actually stored) 142: * 143: * K is the main loop index, decreasing from N in steps of 1 or 2 144: * 145: * KW is the column of W which corresponds to column K of A 146: * 147: K = N 148: 10 CONTINUE 149: KW = NB + K - N 150: * 151: * Exit from loop 152: * 153: IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 ) 154: $ GO TO 30 155: * 156: * Copy column K of A to column KW of W and update it 157: * 158: CALL ZCOPY( K-1, A( 1, K ), 1, W( 1, KW ), 1 ) 159: W( K, KW ) = DBLE( A( K, K ) ) 160: IF( K.LT.N ) THEN 161: CALL ZGEMV( 'No transpose', K, N-K, -CONE, A( 1, K+1 ), LDA, 162: $ W( K, KW+1 ), LDW, CONE, W( 1, KW ), 1 ) 163: W( K, KW ) = DBLE( W( K, KW ) ) 164: END IF 165: * 166: KSTEP = 1 167: * 168: * Determine rows and columns to be interchanged and whether 169: * a 1-by-1 or 2-by-2 pivot block will be used 170: * 171: ABSAKK = ABS( DBLE( W( K, KW ) ) ) 172: * 173: * IMAX is the row-index of the largest off-diagonal element in 174: * column K, and COLMAX is its absolute value 175: * 176: IF( K.GT.1 ) THEN 177: IMAX = IZAMAX( K-1, W( 1, KW ), 1 ) 178: COLMAX = CABS1( W( IMAX, KW ) ) 179: ELSE 180: COLMAX = ZERO 181: END IF 182: * 183: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 184: * 185: * Column K is zero: set INFO and continue 186: * 187: IF( INFO.EQ.0 ) 188: $ INFO = K 189: KP = K 190: A( K, K ) = DBLE( A( K, K ) ) 191: ELSE 192: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 193: * 194: * no interchange, use 1-by-1 pivot block 195: * 196: KP = K 197: ELSE 198: * 199: * Copy column IMAX to column KW-1 of W and update it 200: * 201: CALL ZCOPY( IMAX-1, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 ) 202: W( IMAX, KW-1 ) = DBLE( A( IMAX, IMAX ) ) 203: CALL ZCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA, 204: $ W( IMAX+1, KW-1 ), 1 ) 205: CALL ZLACGV( K-IMAX, W( IMAX+1, KW-1 ), 1 ) 206: IF( K.LT.N ) THEN 207: CALL ZGEMV( 'No transpose', K, N-K, -CONE, 208: $ A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW, 209: $ CONE, W( 1, KW-1 ), 1 ) 210: W( IMAX, KW-1 ) = DBLE( W( IMAX, KW-1 ) ) 211: END IF 212: * 213: * JMAX is the column-index of the largest off-diagonal 214: * element in row IMAX, and ROWMAX is its absolute value 215: * 216: JMAX = IMAX + IZAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 ) 217: ROWMAX = CABS1( W( JMAX, KW-1 ) ) 218: IF( IMAX.GT.1 ) THEN 219: JMAX = IZAMAX( IMAX-1, W( 1, KW-1 ), 1 ) 220: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, KW-1 ) ) ) 221: END IF 222: * 223: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 224: * 225: * no interchange, use 1-by-1 pivot block 226: * 227: KP = K 228: ELSE IF( ABS( DBLE( W( IMAX, KW-1 ) ) ).GE.ALPHA*ROWMAX ) 229: $ THEN 230: * 231: * interchange rows and columns K and IMAX, use 1-by-1 232: * pivot block 233: * 234: KP = IMAX 235: * 236: * copy column KW-1 of W to column KW 237: * 238: CALL ZCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 ) 239: ELSE 240: * 241: * interchange rows and columns K-1 and IMAX, use 2-by-2 242: * pivot block 243: * 244: KP = IMAX 245: KSTEP = 2 246: END IF 247: END IF 248: * 249: KK = K - KSTEP + 1 250: KKW = NB + KK - N 251: * 252: * Updated column KP is already stored in column KKW of W 253: * 254: IF( KP.NE.KK ) THEN 255: * 256: * Copy non-updated column KK to column KP 257: * 258: A( KP, KP ) = DBLE( A( KK, KK ) ) 259: CALL ZCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ), 260: $ LDA ) 261: CALL ZLACGV( KK-1-KP, A( KP, KP+1 ), LDA ) 262: CALL ZCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 ) 263: * 264: * Interchange rows KK and KP in last KK columns of A and W 265: * 266: IF( KK.LT.N ) 267: $ CALL ZSWAP( N-KK, A( KK, KK+1 ), LDA, A( KP, KK+1 ), 268: $ LDA ) 269: CALL ZSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ), 270: $ LDW ) 271: END IF 272: * 273: IF( KSTEP.EQ.1 ) THEN 274: * 275: * 1-by-1 pivot block D(k): column KW of W now holds 276: * 277: * W(k) = U(k)*D(k) 278: * 279: * where U(k) is the k-th column of U 280: * 281: * Store U(k) in column k of A 282: * 283: CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 ) 284: R1 = ONE / DBLE( A( K, K ) ) 285: CALL ZDSCAL( K-1, R1, A( 1, K ), 1 ) 286: * 287: * Conjugate W(k) 288: * 289: CALL ZLACGV( K-1, W( 1, KW ), 1 ) 290: ELSE 291: * 292: * 2-by-2 pivot block D(k): columns KW and KW-1 of W now 293: * hold 294: * 295: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) 296: * 297: * where U(k) and U(k-1) are the k-th and (k-1)-th columns 298: * of U 299: * 300: IF( K.GT.2 ) THEN 301: * 302: * Store U(k) and U(k-1) in columns k and k-1 of A 303: * 304: D21 = W( K-1, KW ) 305: D11 = W( K, KW ) / DCONJG( D21 ) 306: D22 = W( K-1, KW-1 ) / D21 307: T = ONE / ( DBLE( D11*D22 )-ONE ) 308: D21 = T / D21 309: DO 20 J = 1, K - 2 310: A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) ) 311: A( J, K ) = DCONJG( D21 )* 312: $ ( D22*W( J, KW )-W( J, KW-1 ) ) 313: 20 CONTINUE 314: END IF 315: * 316: * Copy D(k) to A 317: * 318: A( K-1, K-1 ) = W( K-1, KW-1 ) 319: A( K-1, K ) = W( K-1, KW ) 320: A( K, K ) = W( K, KW ) 321: * 322: * Conjugate W(k) and W(k-1) 323: * 324: CALL ZLACGV( K-1, W( 1, KW ), 1 ) 325: CALL ZLACGV( K-2, W( 1, KW-1 ), 1 ) 326: END IF 327: END IF 328: * 329: * Store details of the interchanges in IPIV 330: * 331: IF( KSTEP.EQ.1 ) THEN 332: IPIV( K ) = KP 333: ELSE 334: IPIV( K ) = -KP 335: IPIV( K-1 ) = -KP 336: END IF 337: * 338: * Decrease K and return to the start of the main loop 339: * 340: K = K - KSTEP 341: GO TO 10 342: * 343: 30 CONTINUE 344: * 345: * Update the upper triangle of A11 (= A(1:k,1:k)) as 346: * 347: * A11 := A11 - U12*D*U12' = A11 - U12*W' 348: * 349: * computing blocks of NB columns at a time (note that conjg(W) is 350: * actually stored) 351: * 352: DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB 353: JB = MIN( NB, K-J+1 ) 354: * 355: * Update the upper triangle of the diagonal block 356: * 357: DO 40 JJ = J, J + JB - 1 358: A( JJ, JJ ) = DBLE( A( JJ, JJ ) ) 359: CALL ZGEMV( 'No transpose', JJ-J+1, N-K, -CONE, 360: $ A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, CONE, 361: $ A( J, JJ ), 1 ) 362: A( JJ, JJ ) = DBLE( A( JJ, JJ ) ) 363: 40 CONTINUE 364: * 365: * Update the rectangular superdiagonal block 366: * 367: CALL ZGEMM( 'No transpose', 'Transpose', J-1, JB, N-K, 368: $ -CONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW, 369: $ CONE, A( 1, J ), LDA ) 370: 50 CONTINUE 371: * 372: * Put U12 in standard form by partially undoing the interchanges 373: * in columns k+1:n 374: * 375: J = K + 1 376: 60 CONTINUE 377: JJ = J 378: JP = IPIV( J ) 379: IF( JP.LT.0 ) THEN 380: JP = -JP 381: J = J + 1 382: END IF 383: J = J + 1 384: IF( JP.NE.JJ .AND. J.LE.N ) 385: $ CALL ZSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA ) 386: IF( J.LE.N ) 387: $ GO TO 60 388: * 389: * Set KB to the number of columns factorized 390: * 391: KB = N - K 392: * 393: ELSE 394: * 395: * Factorize the leading columns of A using the lower triangle 396: * of A and working forwards, and compute the matrix W = L21*D 397: * for use in updating A22 (note that conjg(W) is actually stored) 398: * 399: * K is the main loop index, increasing from 1 in steps of 1 or 2 400: * 401: K = 1 402: 70 CONTINUE 403: * 404: * Exit from loop 405: * 406: IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N ) 407: $ GO TO 90 408: * 409: * Copy column K of A to column K of W and update it 410: * 411: W( K, K ) = DBLE( A( K, K ) ) 412: IF( K.LT.N ) 413: $ CALL ZCOPY( N-K, A( K+1, K ), 1, W( K+1, K ), 1 ) 414: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ), LDA, 415: $ W( K, 1 ), LDW, CONE, W( K, K ), 1 ) 416: W( K, K ) = DBLE( W( K, K ) ) 417: * 418: KSTEP = 1 419: * 420: * Determine rows and columns to be interchanged and whether 421: * a 1-by-1 or 2-by-2 pivot block will be used 422: * 423: ABSAKK = ABS( DBLE( W( K, K ) ) ) 424: * 425: * IMAX is the row-index of the largest off-diagonal element in 426: * column K, and COLMAX is its absolute value 427: * 428: IF( K.LT.N ) THEN 429: IMAX = K + IZAMAX( N-K, W( K+1, K ), 1 ) 430: COLMAX = CABS1( W( IMAX, K ) ) 431: ELSE 432: COLMAX = ZERO 433: END IF 434: * 435: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN 436: * 437: * Column K is zero: set INFO and continue 438: * 439: IF( INFO.EQ.0 ) 440: $ INFO = K 441: KP = K 442: A( K, K ) = DBLE( A( K, K ) ) 443: ELSE 444: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN 445: * 446: * no interchange, use 1-by-1 pivot block 447: * 448: KP = K 449: ELSE 450: * 451: * Copy column IMAX to column K+1 of W and update it 452: * 453: CALL ZCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 ) 454: CALL ZLACGV( IMAX-K, W( K, K+1 ), 1 ) 455: W( IMAX, K+1 ) = DBLE( A( IMAX, IMAX ) ) 456: IF( IMAX.LT.N ) 457: $ CALL ZCOPY( N-IMAX, A( IMAX+1, IMAX ), 1, 458: $ W( IMAX+1, K+1 ), 1 ) 459: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ), 460: $ LDA, W( IMAX, 1 ), LDW, CONE, W( K, K+1 ), 461: $ 1 ) 462: W( IMAX, K+1 ) = DBLE( W( IMAX, K+1 ) ) 463: * 464: * JMAX is the column-index of the largest off-diagonal 465: * element in row IMAX, and ROWMAX is its absolute value 466: * 467: JMAX = K - 1 + IZAMAX( IMAX-K, W( K, K+1 ), 1 ) 468: ROWMAX = CABS1( W( JMAX, K+1 ) ) 469: IF( IMAX.LT.N ) THEN 470: JMAX = IMAX + IZAMAX( N-IMAX, W( IMAX+1, K+1 ), 1 ) 471: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, K+1 ) ) ) 472: END IF 473: * 474: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN 475: * 476: * no interchange, use 1-by-1 pivot block 477: * 478: KP = K 479: ELSE IF( ABS( DBLE( W( IMAX, K+1 ) ) ).GE.ALPHA*ROWMAX ) 480: $ THEN 481: * 482: * interchange rows and columns K and IMAX, use 1-by-1 483: * pivot block 484: * 485: KP = IMAX 486: * 487: * copy column K+1 of W to column K 488: * 489: CALL ZCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 ) 490: ELSE 491: * 492: * interchange rows and columns K+1 and IMAX, use 2-by-2 493: * pivot block 494: * 495: KP = IMAX 496: KSTEP = 2 497: END IF 498: END IF 499: * 500: KK = K + KSTEP - 1 501: * 502: * Updated column KP is already stored in column KK of W 503: * 504: IF( KP.NE.KK ) THEN 505: * 506: * Copy non-updated column KK to column KP 507: * 508: A( KP, KP ) = DBLE( A( KK, KK ) ) 509: CALL ZCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ), 510: $ LDA ) 511: CALL ZLACGV( KP-KK-1, A( KP, KK+1 ), LDA ) 512: IF( KP.LT.N ) 513: $ CALL ZCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 ) 514: * 515: * Interchange rows KK and KP in first KK columns of A and W 516: * 517: CALL ZSWAP( KK-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA ) 518: CALL ZSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW ) 519: END IF 520: * 521: IF( KSTEP.EQ.1 ) THEN 522: * 523: * 1-by-1 pivot block D(k): column k of W now holds 524: * 525: * W(k) = L(k)*D(k) 526: * 527: * where L(k) is the k-th column of L 528: * 529: * Store L(k) in column k of A 530: * 531: CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 ) 532: IF( K.LT.N ) THEN 533: R1 = ONE / DBLE( A( K, K ) ) 534: CALL ZDSCAL( N-K, R1, A( K+1, K ), 1 ) 535: * 536: * Conjugate W(k) 537: * 538: CALL ZLACGV( N-K, W( K+1, K ), 1 ) 539: END IF 540: ELSE 541: * 542: * 2-by-2 pivot block D(k): columns k and k+1 of W now hold 543: * 544: * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) 545: * 546: * where L(k) and L(k+1) are the k-th and (k+1)-th columns 547: * of L 548: * 549: IF( K.LT.N-1 ) THEN 550: * 551: * Store L(k) and L(k+1) in columns k and k+1 of A 552: * 553: D21 = W( K+1, K ) 554: D11 = W( K+1, K+1 ) / D21 555: D22 = W( K, K ) / DCONJG( D21 ) 556: T = ONE / ( DBLE( D11*D22 )-ONE ) 557: D21 = T / D21 558: DO 80 J = K + 2, N 559: A( J, K ) = DCONJG( D21 )* 560: $ ( D11*W( J, K )-W( J, K+1 ) ) 561: A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) ) 562: 80 CONTINUE 563: END IF 564: * 565: * Copy D(k) to A 566: * 567: A( K, K ) = W( K, K ) 568: A( K+1, K ) = W( K+1, K ) 569: A( K+1, K+1 ) = W( K+1, K+1 ) 570: * 571: * Conjugate W(k) and W(k+1) 572: * 573: CALL ZLACGV( N-K, W( K+1, K ), 1 ) 574: CALL ZLACGV( N-K-1, W( K+2, K+1 ), 1 ) 575: END IF 576: END IF 577: * 578: * Store details of the interchanges in IPIV 579: * 580: IF( KSTEP.EQ.1 ) THEN 581: IPIV( K ) = KP 582: ELSE 583: IPIV( K ) = -KP 584: IPIV( K+1 ) = -KP 585: END IF 586: * 587: * Increase K and return to the start of the main loop 588: * 589: K = K + KSTEP 590: GO TO 70 591: * 592: 90 CONTINUE 593: * 594: * Update the lower triangle of A22 (= A(k:n,k:n)) as 595: * 596: * A22 := A22 - L21*D*L21' = A22 - L21*W' 597: * 598: * computing blocks of NB columns at a time (note that conjg(W) is 599: * actually stored) 600: * 601: DO 110 J = K, N, NB 602: JB = MIN( NB, N-J+1 ) 603: * 604: * Update the lower triangle of the diagonal block 605: * 606: DO 100 JJ = J, J + JB - 1 607: A( JJ, JJ ) = DBLE( A( JJ, JJ ) ) 608: CALL ZGEMV( 'No transpose', J+JB-JJ, K-1, -CONE, 609: $ A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, CONE, 610: $ A( JJ, JJ ), 1 ) 611: A( JJ, JJ ) = DBLE( A( JJ, JJ ) ) 612: 100 CONTINUE 613: * 614: * Update the rectangular subdiagonal block 615: * 616: IF( J+JB.LE.N ) 617: $ CALL ZGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, 618: $ K-1, -CONE, A( J+JB, 1 ), LDA, W( J, 1 ), 619: $ LDW, CONE, A( J+JB, J ), LDA ) 620: 110 CONTINUE 621: * 622: * Put L21 in standard form by partially undoing the interchanges 623: * in columns 1:k-1 624: * 625: J = K - 1 626: 120 CONTINUE 627: JJ = J 628: JP = IPIV( J ) 629: IF( JP.LT.0 ) THEN 630: JP = -JP 631: J = J - 1 632: END IF 633: J = J - 1 634: IF( JP.NE.JJ .AND. J.GE.1 ) 635: $ CALL ZSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA ) 636: IF( J.GE.1 ) 637: $ GO TO 120 638: * 639: * Set KB to the number of columns factorized 640: * 641: KB = K - 1 642: * 643: END IF 644: RETURN 645: * 646: * End of ZLAHEF 647: * 648: END